Re: Finite dimensional vector space

Frrom Wolfram Mathworld: "Finite set: A set whose elements can be numbered through from 1 to , for some positive integer ." Which is same as def from Birkhoff-McLane.

HOWEVER Kelley (Topology) gives a definition of a finite set which is unintelligible unless you have the time and interest to learn the language, which you can do in one of two ways depending on how your brain works:

1) Memorize words and symbols, their parts of speech, and the rules of the "grammar." In this way you will always put together a logical sentence, which others will recognize as logical. You could accidentally put together a sentence like "the dog is a cat," or the most profound thought in the history of the world.

2) Same as above but you also try for some meaning to the words.

I don't have the brain for 1) and some trouble with 2), which is why I look for the minimum number of meaningful concepts with the greatest relevance.

A link to a page written in a language I don't know doesn't help me much.

EDIT If the elements are books, and a bag has a finite number of books, a book has to exist in order to create a one-one correspondence with it. Is a book with the characteristic that it doesn't exist a book?